Complex Numbers (Book)

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Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

October 27, 2021 at 12:01am

#1020216

The Play's the Thing

I mean, aren't we always quoting Shakespeare?

21 Phrases You Use Without Realizing You're Quoting William Shakespeare

William Shakespeare devised new words and countless plot tropes that still appear in everyday life.

And yet, when I devise a new word, people tell me I don't speak English good.

But an incredible number of lines from his plays have become so ingrained into modern vernacular that we no longer recognize them as lines from plays at all.

One wonders if he really did coin these phrases or adapted them from the vernacular. It's like... if someone's passing a meme around, and I put it in a book, and somehow the internet dies but the book survives, in five hundred years will they say I invented the phrase from the meme?

...probably not; they'll just assume I lifted it from somewhere. But for some reason Shakespeare gets the benefit of the doubt there.

I'm not going to quote all of them, just my thoughts on a few.

2. "GREEN-EYED MONSTER" // OTHELLO, ACT III, SCENE III

Before Shakespeare, the color green was most commonly associated with illness.

Coincidentally, just this evening, I was perusing the contents of my liquor cabinet and went, "Hm. I wonder what would happen if I mixed this absinthe with that Midori?" (Both are green, if you don't know.) And now at least I know what to call it when I concoct that unholy abomination, probably right after I publish this.

3. "PURE AS THE DRIVEN SNOW" // HAMLET, ACT III, SCENE I AND THE WINTER'S TALE, ACT IV, SCENE IV

For the record, this simile works best right after the snow falls, and not a few hours later when tires and footprints turn it into brown slush.

But then it's not "driven" snow, is it? IS IT? Before cars, "driving" meant driving a team of horses (or other animals like oxen or whatever), maybe in front of a carriage or plow. Driven snow is thus snow that has been driven on. At least that's the interpretation I use; I just assume "pure as the driven snow" is sarcasm, like "clear as mud" or "smooth as sandpaper." But then, I'm of the considered opinion that Romeo and Juliet is best viewed as satire.

7. "GOOD RIDDANCE" // TROILUS AND CRESSIDA, ACT II, SCENE I

Bye, Felicia.

13. "LOVE IS BLIND" // THE MERCHANT OF VENICE, ACT II, SCENE VI

Chaucer actually wrote the phrase ("For loue is blynd alday and may nat see") in The Merchant’s Tale in 1405, but it didn't become popular and wasn't seen in print again until Shakespeare wrote it down.

More likely, love is deaf. I mean, who hasn't fallen into a thirst trap and ended up missing red flags because they're just so damn hot? Too much looking, not enough listening.

Also, remember what I said about maybe Shakespeare didn't coin all of these? Well.

21. "THE GAME IS AFOOT" // HENRY V, ACT III, SCENE I

Nope! It wasn't Sir Arthur Conan Doyle who coined this phrase—Sherlock Holmes' most famous catchphrase comes from Henry V...

At some point, somewhere, I wrote "the foot is a game!" in a zombie story. Can't for the life of me find it now, or remember what it was about. It's not on WDC.

So anyway, short but interesting article for Shakespeare, idiom, and cliché fans.

4 Like • Comment • View 4 comments

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